化简求值，【（x-1/x）-（x-2/x+1）】÷（2x²-x/x²+2x+1），其中x满足x²-x-1=0
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数学之美团为你解答
[ (x-1)/x - (x-2)/(x+1) ] ÷ (2x²-x)/(x²+2x+1)
= [(x-1)(x+1) - x(x-2)] / [x(x+1)] ÷ [ x(2x-1)/(x+1)² ]
= (x²-1-x²+2x) / [x(x+1)] ÷ [ x(2x-1)/(x+1)² ]
= (2x-1) / [x(x+1)] * (x+1)² / [x(2x-1)]
= (x+1)/x²
∵x²-x-1=0 即 x² = x+1
∴原式 = 1
数学之美团为你解答
[ (x-1)/x - (x-2)/(x+1) ] ÷ (2x²-x)/(x²+2x+1)
= [(x-1)(x+1) - x(x-2)] / [x(x+1)] ÷ [ x(2x-1)/(x+1)² ]
= (x²-1-x²+2x) / [x(x+1)] ÷ [ x(2x-1)/(x+1)² ]
= (2x-1) / [x(x+1)] * (x+1)² / [x(2x-1)]
= (x+1)/x²
∵x²-x-1=0 即 x² = x+1
∴原式 = 1
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